 | John Playfair - Euclid's Elements - 1846 - 332 pages
...DAC is a right angle ; therefore also BAC is a right angle. ADDITIONAL PROPOSITIONS. PROP. A. THEOR. A perpendicular is the shortest line that can be drawn from a point, situated without a straight line, to that line : any two oblique lines drawn from the same point... | |
 | George Roberts Perkins - Geometry - 1847 - 308 pages
...sum of the angles CBF and FBD, that is, to the whole angle CBD (Ax. II), PROPOSITION XXVI. THEOREM. A perpendicular is the shortest line that can be drawn from a given point to a line of indefinite length ; and of any other lines drawn from the same point, those that are nearest... | |
 | Charles William Hackley - Geometry - 1847 - 248 pages
...double the number of sides and subtract 4, the right angle being the unit of measure.! THEOREM XVII. A perpendicular is the shortest line that can be drawn from a given point to an indefinite line. And, of any other lines drawn from the same point, those that are equally distant... | |
 | Charles Davies - Geometry - 1850 - 236 pages
...exceed two right angles : hence, at least two angles of every triangle must be acute. THEOREM XVIII. I. A perpendicular is the shortest line that can be...of lines be drawn from the same point, those which are nearest the perpendicular are less than those which arc more remote. Of Triangles. drawn : Then,... | |
 | Charles Davies - Geometry - 1850 - 218 pages
...exceed two right angles : hence, at least two angles of every triangle must be acute. THEOREM XVIII. I. A perpendicular is the shortest line that can be...of lines be drawn from the same point, those which are nearest the perpendicular are less than those which are more remote. Of Triangles. drawn : Then,... | |
 | George Roberts Perkins - Geometry - 1850 - 332 pages
...sum of the angles CBF and FBD, that is, to the whole angle CBD, (Ax. II.) PROPOSITION XXVI. THEOREM. A perpendicular is the shortest line that can be drawn from a given point to a line of indefinite length ; and of any other lines drawn from the same point, those that are nearest... | |
 | Euclides - 1860 - 142 pages
...it passes through the point O, the same reasoning will apply. EXERCISE V. — THEOREM. Of all lines that can be drawn from a given point to a given line, the perpendicular upon it is the least; and of all others, that which is nearer to the perpendicular... | |
 | Horatio Nelson Robinson - Geometry - 1860 - 472 pages
...opposite the greater angle, AB is less than AC; and AC may be any line not identical with AB; therefore a perpendicular is the shortest line that can be drawn from A to the line DE. 2d. As the two angles, ACB and ACD, are together equal to two right angles, (Th. 1),... | |
 | Euclides - 1865 - 402 pages
...than two right angles, by joining A to any point in BC. 18. The perpendicular is the shortest straight line that can be drawn from a given point to a given straight line ; and of others, that which is nearer to the perpendicular is less than the more remote... | |
 | C. Davies - 1867 - 342 pages
...exceed two right angles : hence, at least two angles of every triangle must be acuteTHEOREM XVIIII A perpendicular is the shortest line that can be drawn from a given point to a given lineII If any number of lines be drawn from the- same point, those which arc nearest the perpendicular... | |
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The perpendicular is the shortest straight line that can be drawn from a given point to a given straight line; and... 
